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Science, Religion, and Secularism Part VII: Plato and the Geometric Model of Knowledge

October 29, 2017 by Daniel Halverson 1 Comment

In order to better appreciate the relationship between the collections of knowledge claims, today labeled “science” and “religion,” it may be helpful to take a step back and look at the category of knowledge itself. What do we know, and under what circumstances can we be said to know it? A historical approach to this question will eschew normative claims about true, justified belief, and focus instead on the task of description. In other words, it will not ask what should count as knowledge, but what has in the past, on what plausible basis those claims have rested, and through what changes the present constitution of knowledge has come about.

In very broad terms, one of the chief conclusions of the philosophical debates that occurred in ancient Greece, from the time of the Presocratics (sixth century BCE) to that of Aristotle (fourth century CE), was that geometry had the best claim to knowledge. “Geometry will draw the soul toward truth, and create the spirit of philosophy,” Plato wrote in the Republic. Later, an inscription above the door of the Academy named after him read: "Let no one ignorant of geometry enter.” So, geometry was very important to Plato, who has in turn been very important to Western philosophy. Even people who profoundly disagree with Plato are usually forced to mention him—if only to define themselves against him!

While it might seem that geometry is an abstract kind of knowledge and not very relevant to our everyday lives—how many school children have protested at having to learn the Pythagorean theorem with the rhetorical question, “When am I ever going to use this?”—a little reflection shows that it has at least two important attractions. For one thing, it doesn’t require a lot of expensive equipment, collaborators, or institutional support. Anyone with a passion for the subject and sufficient time on their hands can pursue this kind of knowledge, and perhaps make a contribution to it. For another, it’s certain. To understand the definition of the term “triangle” is to understand why, necessarily, a triangle has three sides. Further investigation shows that it is also a necessary (though not, at first, an obvious) consequence of that definition that its interior angles add up to one hundred and eighty degrees. Finally, geometric knowledge is permanent. When it can be shown that a definition necessarily entails certain consequences, no further demonstration or revision is necessary; the scope of human understanding has been irreversibly enlarged, so long as that knowledge remains accessible. So geometry conforms very well to, and perhaps helped to bring about, Greek ideals about knowledge—namely, that genuine knowledge is self-sufficient, certain, and permanent. When the Greek geometer Archimedes had his formulae for the derivation of the volume of a cube and a cylinder stamped on his tomb, he was boasting of just this type of accomplishment.

What we moderns often dismiss as speculative, useless metaphysics was, until quite recently, the surest path to knowledge.

None of this is to say that the Greeks thought that the most important kind of knowledge had to do with triangles and squares. History is strange, but not that strange! People in ancient Greece wondered, as people have in other times and places, about the big questions.” What is the nature of truth? What does it mean to live a good life? How can I know right from wrong? What should we think of the gods our ancestors worshipped? None of these questions are addressed by geometry, or conceivably, could be. But the geometric model could be, and was, imported. Plato’s insight was that if a priori, deductive methods proceeding from definitions and terminating in claims about what must necessarily and always be the case—if these methods had proven successful in one area of knowledge, they might prove successful in others as well. All of knowledge might potentially be assimilated to the model of geometry. What we moderns often dismiss as speculative, useless metaphysics was, until quite recently, the surest path to knowledge.

In the fourth century BCE, the Macedonian king Alexander the Great conquered Greece, then the Persian Empire, and even parts of India. When he died, his generals divvied up his empire and a Greek-speaking, warrior aristocracy ruled the Eastern Mediterranean for several centuries. Since the Greeks were proud of their culture, with its rich mathematical, philosophical, and artistic heritage, they set up schools and academies and other places of learning—most famously the Great Library of Alexandria. Greek culture spread from these institutions to the whole of the Eastern Mediterranean. The Romans conquered these Greek successor states in the first century BCE, and incorporated them into their empire. The Roman aristocracy valued Greek learning, and preserved it. An educated Roman was supposed to know how to speak and read the Greek language, but Greek was never widely adopted in the Western half of the Empire. There, the peoples whom the Roman Empire conquered increasingly had to learn Latin in order to get along. Hence the Roman Empire was essentially a bilingual entity: a Latin-speaking West fused to a Greek-speaking East. But there was never parity between Greek and Latin in terms of cultural value. Latin may have been the language of governance, but Greek was the language of learning.

Hence the rise of Christianity occurred within a society where serious intellectual activity was dominated by the Greek language and Greek thought, which in turn was dominated by the philosophy of Plato and his heirs. This presented both a challenge and an opportunity to the leaders of the new faith. On the one hand, their Scriptures and Messiah were emphatically Hebraic, not Greek, in origin. On the other, they wanted their faith to have credibility in a cultural environment dominated by Greek thought. Although there were some dissenters—Tertullian famously asked, “What does Athens have to do with Jerusalem?”—their general program was to attempt a fusion. Origen, Augustine, Maximos, and the other “Church Fathers,” as they came to be called, appropriated Greek, Platonic philosophy—especially in the form given to it by the Alexandrian philosopher Plotinus—and attempted to reconcile it with the Hebraic tradition, as preserved in the prophetic and messianic books that were being assembled, in those same centuries, into the library of documents that we know as the Bible.

This was, needless to say, an extremely complicated project, and its vicissitudes cannot detain us. The main challenge was that Hebraic thought had a very different orientation than Greek. It was not concerned with the timeless, abstract forms of Plato, but with the historical, concrete relationship of the chosen people to their God. The “God of the philosophers”—that contemplated by Plato, Plotinus, Spinoza, and Voltaire—was serene, complete, static, perfect, and utterly remote in transcendence. This view of God was difficult to reconcile with God of the Hebrews, who was very much involved with the affairs of the world, and who was known not through contemplation of the forms, but through the utterances of prophets and the fortunes of the chosen people.

How successful this project was, or is, individuals can evaluate for themselves. From a historical point of view, what is of interest is that this fusion set the tone for serious intellectual activity in both the Latin- and Greek-speaking halves of the Western world for centuries. Christian theology, modeled in part on the transcendental geometry of the Greeks, and in part on the sacred history of the Hebrews, became the most influential and widespread set of knowledge claims both within, and in some cases beyond the frontiers of, the Roman Empire. Natural philosophy, the progenitor to modern science, existed, but not in anything like the form we have it today. Its usefulness and importance, so far from being taken for granted in the ancient world, were not even seriously entertained.

In future articles, we’ll look at the rise of science, and what it has meant for theology as well as for other sets of knowledge claims. But before moving on to this exciting and important topic, I hope I can interest you in a classic of intellectual history that explores a little-known, but in its time an enormously-influential, aspect of Plato’s philosophy. In the next articles we’ll begin to explore Arthur O. Lovejoy’s brilliant genealogy of one of Plato’s most enduring ideas—the great chain of being.

This essay is part of a series; the previous essay can be found here.

Daniel Halverson is a graduate student studying the History of Science and Technology. He is also a regular contributor to the PEL Facebook page. 


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Filed Under: Misc. Philosophical Musings Tagged With: philosophy blog, philosophy of religion, philosophy of science, Plato

Comments

  1. Evan Hadkins says

    November 2, 2017 at 9:55 pm

    Typo Aristotle’s dates are BCE no CE

    Reply

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